Question

Triangle X Y Z is shown. The length of side X Y is (9 n + 12) feet and the length of side X Z is (15 n minus 6) feet. Angles X Y Z and Y Z X are congruent. Consider isosceles ΔXYZ. What is the value of n? What is the measure of leg XY? ft What is the measure of leg XZ? ft

Answer 1

Answer:

$n = 3$

$XY = 39$

$XZ = 39$

Step-by-step explanation:

Given

$XY = 9n + 12$

$XZ = 15n - 6$

Solving (a): n

To solve for n;

We make use of

$XY = XZ$

Substitute values for XY and XZ

$9n + 12 = 15n - 6$

$9n - 15n = -12 - 6$

$-6n = -18$

Divide through by -6

$n = 3$

Solving (b) XY

$XY = 9n + 12$

Substitute 3 for n

$XY = 9 * 3 + 12$

$XY = 27 + 12$

$XY = 39$

Solving (c): XZ

$XZ = XY$

$XZ = 39$